Hi,
If you are using zfs, i think the best solution could be snapshot and export the snapshot to another file system. But if you are thinking about the filesystem backup then the best solution can be Bacula system.
Regards.
As noted by @cemzafer, the snapshot method seems to be the best.
We have been using this approach for a while and its very effective as you want to avoid downtime
Create the snapshot lxc snapshot container_name snapshot_name
Snapshot to Image lxc publish container_name/snapshot_name --alias exported_image
Convert your Image to File lxc image export exported_image exported_image.tar.gz
You can write move your image to your backup storage